Finite Group Databasebeta

← C7×#23525 #13200741

Subgroups — C7×#23525 #13200741

Order 1792.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#575C211yesmaximal, characteristic
2C2×C7×#430C211yesmaximal, characteristic, complemented
3C2×C7×#421C211yesmaximal, characteristic, complemented
4C7×#2896C211yesmaximal, characteristic, complemented
5C2×C7×#413C211yesmaximal, characteristic, complemented
6C2×C7×#413C211yesmaximal, characteristic, complemented
7C7×#2049C214yesmaximal, complemented
8C7×#2048C214yesmaximal, complemented
9C2×C7×#344C211yesmaximal, characteristic, complemented
10C22×C7×#41C2211yescharacteristic
11C22×C7×#41C2211yescharacteristic
12C7×#575—22no—
13C7×#575—22no—
14C7×#575—22no—
15C7×#575—22no—
16C2×C7×#137—21no—
17C2×C7×#137C2212yes—
18C2×C7×AGL(1,ℤ/8)—21no—
19C2×C7×AGL(1,ℤ/8)C2212yes—
20C2×C7×#135—22no—
21C22×C7×M16C2211yescharacteristic
22C22×C7×M16C2211yescharacteristic
23C22×C7×M16C2211yescharacteristic
24C22×C7×M16C2211yescharacteristic
25C2×C7×#117C2211yescharacteristic
26C7×#430—22no—
27C7×#430C2214yescomplemented
28C2×C7×#108—22no—
29C7×#421—22no—
30C7×#421C2214yes—
31C2×C7×#104—22no—
32C7×#419C2212yescomplemented
33C7×#418C2212yescomplemented
34C7×#417—22no—
35C7×#416—22no—
36C7×#413—22no—
37C7×#413—22no—
38C7×#413—22no—
39C7×#413C2214yes—
40C2×C7×#101—21no—
41C2×C7×#101C2212yescomplemented
42C2×C7×#100—21no—
43C2×C7×#100C2212yescomplemented
44C7×#344C2214yescomplemented
45#23525C711yesmaximal, characteristic, direct product factor, Sylow
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—21no—
63C2×C7×#41—21no—
64C2×C7×#41—21no—
65C2×C7×#41—21no—
66C2×C7×#41D412yes—
67C2×C7×#41D412yes—
68C2×C7×#41D412yes—
69C2×C7×#41C2312yes—
70C22×C7×Q8D411yescharacteristic
71C22×C7×Q8C2311yescharacteristic
72C22×C7×D4—21no—
73C22×C7×D4—21no—
74C22×C7×D4D411yescharacteristic
75C22×C7×D4C2311yescharacteristic
76C23×C4×C7—21no—
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C7×#137—24no—
80C7×#137—24no—
81C7×#137—24no—
82C7×#137—24no—
83C7×AGL(1,ℤ/8)—24no—
84C7×AGL(1,ℤ/8)—24no—
85C7×AGL(1,ℤ/8)—24no—
86C7×AGL(1,ℤ/8)—24no—
87C7×#135—28no—
88C7×#135—28no—
89C2×C7×Q16—22no—
90C2×C7×SD16—22no—
91C2×C7×SD16—22no—
92C2×C7×D8—22no—
93C2×C7×M16—21no—
94C2×C7×M16—21no—
95C2×C7×M16—21no—
96C2×C7×M16—21no—
97C2×C7×M16—21no—
98C2×C7×M16—21no—
99C2×C7×M16—21no—
100C2×C7×M16—21no—
101C2×C7×M16—21no—
102C2×C7×M16—21no—
103C2×C7×M16—21no—
104C2×C7×M16—21no—
105C2×C7×M16—21no—
106C2×C7×M16—21no—
107C2×C7×M16—21no—
108C2×C7×M16—21no—
109C2×C7×M16D412yes—
110C2×C7×M16D412yes—
111C2×C7×M16D412yes—
112C2×C7×M16D412yes—
113C2×C7×M16C2312yes—
114C2×C7×M16C2312yes—
115C2×C7×M16C2312yes—
116C2×C7×M16C2312yes—
117C22×C7×C8—21no—
118C22×C7×C8—21no—
119C22×C7×C8—21no—
120C22×C7×C8—21no—
121C7×#117—21no—
122C7×#117—21no—
123C7×#117—21no—
124C7×#117C2312yes—
125C2×C7×C4⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C42×C7—21no—
128C7×#108—28no—
129C7×#104—28no—
130C7×#103—24no—
131C7×#102—24no—
132C7×#101—24no—
133C7×#101—24no—
134C7×#100—24no—
135C7×#100—24no—
136C2×#575C2×C711yescharacteristic
137C2×#430C2×C711yescharacteristic, complemented
138C2×#421C2×C711yescharacteristic, complemented
139#2896C2×C711yescharacteristic, complemented
140C2×#413C2×C711yescharacteristic, complemented
141C2×#413C2×C711yescharacteristic, complemented
142#2049C2×C714yescomplemented
143#2048C2×C714yescomplemented
144C2×#344C2×C711yescharacteristic, complemented
145C24×C7—21no—
146C24×C7—21no—
147C24×C7#4111yescharacteristic
148C7×#41—22no—
149C7×#41—22no—
150C7×#41—22no—
151C7×#41—22no—
152C7×#41—22no—
153C7×#41—22no—
154C7×#41—22no—
155C7×#41—22no—
156C7×#41—22no—
157C7×#41—22no—
158C7×#41—22no—
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—22no—
162C7×#41—22no—
163C7×#41—22no—
164C7×#41—41no—
165C7×#41—41no—
166C7×#41—41no—
167C7×#41—41no—
168C7×#41—41no—
169C7×#41—41no—
170C7×#41—41no—
171C7×#41—41no—
172C7×#41—41no—
173C7×#41—41no—
174C7×#41—41no—
175C7×#41—41no—
176C7×#41—41no—
177C7×#41—41no—
178C7×#41—41no—
179C7×#41—41no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—21no—
189C2×C7×Q8—21no—
190C2×C7×Q8C2×D412yes—
191C2×C7×Q8C2×D412yes—
192C2×C7×D4—22no—
193C2×C7×D4—22no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—21no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—41no—
207C2×C7×D4—41no—
208C2×C7×D4—41no—
209C2×C7×D4—41no—
210C2×C7×D4—41no—
211C2×C7×D4—41no—
212C2×C7×D4—41no—
213C2×C7×D4—41no—
214C2×C7×D4C2×D412yes—
215C2×C7×D4C2×D412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—41no—
223C22×C4×C7—41no—
224C22×C4×C7—41no—
225C22×C4×C7—41no—
226C22×C4×C7—41no—
227C22×C4×C7—41no—
228C22×C4×C7—41no—
229C22×C4×C7—41no—
230C22×C4×C7—41no—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7#4111yescharacteristic
240C22×C4×C7#4111yescharacteristic
241C22×C4×C7#4111yescharacteristic
242C22×C4×C7#4111yescharacteristic
243C22×C4×C7#4111yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C7×Q16—28no—
246C7×SD16—28no—
247C7×SD16—28no—
248C7×D8—28no—
249C7×M16—22no—
250C7×M16—22no—
251C7×M16—22no—
252C7×M16—22no—
253C7×M16—22no—
254C7×M16—22no—
255C7×M16—22no—
256C7×M16—22no—
257C7×M16—22no—
258C7×M16—22no—
259C7×M16—41no—
260C7×M16—41no—
261C7×M16—41no—
262C7×M16—41no—
263C7×M16C2×D414yes—
264C7×M16C2×D414yes—
265C2×C7×C8—22no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8—22no—
270C2×C7×C8—22no—
271C2×C7×C8—22no—
272C2×C7×C8—22no—
273C2×C7×C8—41no—
274C2×C7×C8—41no—
275C2×C7×C8—41no—
276C2×C7×C8—41no—
277C7×C4⋊C4—22no—
278C7×C4⋊C4—41no—
279C7×C22⋊C4—22no—
280C7×C22⋊C4—41no—
281C42×C7—22no—
282C42×C7—41no—
283C22×#41C22×C711yescharacteristic
284C22×#41C22×C711yescharacteristic
285#575—22no—
286#575—22no—
287#575—22no—
288#575—22no—
289C2×#137—21no—
290C2×#137C22×C712yes—
291C2×AGL(1,ℤ/8)—21no—
292C2×AGL(1,ℤ/8)C22×C712yes—
293C2×#135—22no—
294C22×M16C22×C711yescharacteristic
295C22×M16C22×C711yescharacteristic
296C22×M16C22×C711yescharacteristic
297C22×M16C22×C711yescharacteristic
298C2×#117C22×C711yescharacteristic
299#430—22no—
300#430C22×C714yescomplemented
301C2×#108—22no—
302#421—22no—
303#421C22×C714yes—
304C2×#104—22no—
305#419C22×C712yescomplemented
306#418C22×C712yescomplemented
307#417—22no—
308#416—22no—
309#413—22no—
310#413—22no—
311#413—22no—
312#413C22×C714yes—
313C2×#101—21no—
314C2×#101C22×C712yescomplemented
315C2×#100—21no—
316C2×#100C22×C712yescomplemented
317#344C22×C714yescomplemented
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—81no—
325C23×C7—82no—
326C23×C7—82no—
327C23×C7#12111yescharacteristic
328C23×C7#12111yescharacteristic
329C23×C7#12311yescharacteristic
330C23×C7#12311yescharacteristic
331C23×C7#12411yescharacteristic
332C23×C7#12411yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C7×Q8—22no—
335C7×Q8—22no—
336C7×Q8—22no—
337C7×Q8—22no—
338C7×Q8—41no—
339C7×Q8—41no—
340C7×Q8—41no—
341C7×Q8—41no—
342C7×D4—22no—
343C7×D4—22no—
344C7×D4—22no—
345C7×D4—22no—
346C7×D4—42no—
347C7×D4—42no—
348C7×D4—42no—
349C7×D4—42no—
350C7×D4—42no—
351C7×D4—42no—
352C7×D4—42no—
353C7×D4—42no—
354C7×D4—41no—
355C7×D4—41no—
356C7×D4—41no—
357C7×D4—41no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—82no—
374C2×C4×C7#12011yescharacteristic
375C2×C4×C7#12011yescharacteristic
376C2×C4×C7#12011yescharacteristic
377C2×C4×C7#12011yescharacteristic
378C2×C4×C7#12111yescharacteristic
379C2×C4×C7#12111yescharacteristic
380C2×C4×C7#12111yescharacteristic
381C2×C4×C7#12111yescharacteristic
382C2×C4×C7#12111yescharacteristic
383C2×C4×C7#12111yescharacteristic
384C2×C4×C7#12111yescharacteristic
385C2×C4×C7#12111yescharacteristic
386C2×C4×C7#12111yescharacteristic
387C2×C4×C7#12111yescharacteristic
388C2×C4×C7#12311yescharacteristic
389C2×C4×C7#12311yescharacteristic
390C2×C4×C7#12311yescharacteristic
391C2×C4×C7#12311yescharacteristic
392C2×C4×C7#12311yescharacteristic
393C2×C4×C7#12311yescharacteristic
394C2×C4×C7#12411yescharacteristic
395C2×C4×C7#12411yescharacteristic
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C22×D411yescharacteristic
399C2×C4×C7C22×D411yescharacteristic
400C2×C4×C7C2×#4111yescharacteristic
401C2×C4×C7C2×#4111yescharacteristic
402C7×C8—24no—
403C7×C8—24no—
404C7×C8—42no—
405C7×C8—42no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41C7×D412yes—
427C2×#41C7×D412yes—
428C2×#41C7×D412yes—
429C2×#41C23×C712yes—
430C22×Q8C7×D411yescharacteristic
431C22×Q8C23×C711yescharacteristic
432C22×D4—21no—
433C22×D4—21no—
434C22×D4C7×D411yescharacteristic
435C22×D4C23×C711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C711yescharacteristic
439#137—24no—
440#137—24no—
441#137—24no—
442#137—24no—
443AGL(1,ℤ/8)—24no—
444AGL(1,ℤ/8)—24no—
445AGL(1,ℤ/8)—24no—
446AGL(1,ℤ/8)—24no—
447#135—28no—
448#135—28no—
449C2×Q16—22no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×D8—22no—
453C2×M16—21no—
454C2×M16—21no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16C7×D412yes—
470C2×M16C7×D412yes—
471C2×M16C7×D412yes—
472C2×M16C7×D412yes—
473C2×M16C23×C712yes—
474C2×M16C23×C712yes—
475C2×M16C23×C712yes—
476C2×M16C23×C712yes—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117C23×C712yes—
485C2×C4⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488#108—28no—
489#104—28no—
490#103—24no—
491#102—24no—
492#101—24no—
493#101—24no—
494#100—24no—
495#100—24no—
496C22×C7—41no—
497C22×C7—41no—
498C22×C7—41no—
499C22×C7—41no—
500C22×C7—41no—
501C22×C7—41no—
502C22×C7—41no—
503C22×C7—42no—
504C22×C7—42no—
505C22×C7—82no—
506C22×C7—82no—
507C22×C7—82no—
508C22×C7—82no—
509C22×C7—82no—
510C22×C7—82no—
511C22×C7#39411yescharacteristic
512C22×C7#39411yescharacteristic
513C22×C7#39411yescharacteristic
514C22×C7#39411yescharacteristic
515C22×C7C2×#12111yescharacteristic
516C22×C7C2×#12311yescharacteristic
517C22×C7C2×#12411yescharacteristic
518C4×C7—42no—
519C4×C7—42no—
520C4×C7—82no—
521C4×C7#39411yescharacteristic
522C4×C7#39411yescharacteristic
523C4×C7#39411yescharacteristic
524C4×C7#39411yescharacteristic
525C4×C7C2×#12011yescharacteristic
526C4×C7C2×#12111yescharacteristic
527C4×C7C2×#12111yescharacteristic
528C4×C7C2×#12311yescharacteristic
529C24—21no—
530C24—21no—
531C24C7×#4111yescharacteristic
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8C2×C7×D412yes—
575C2×Q8C2×C7×D412yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4C2×C7×D412yes—
599C2×D4C2×C7×D412yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4C2×C7×D411yescharacteristic
616C22×C4C2×C7×D411yescharacteristic
617C22×C4C2×C7×D411yescharacteristic
618C22×C4C2×C7×D411yescharacteristic
619C22×C4C2×C7×D411yescharacteristic
620C22×C4C2×C7×D411yescharacteristic
621C22×C4C2×C7×D411yescharacteristic
622C22×C4C2×C7×D411yescharacteristic
623C22×C4C7×#4111yescharacteristic
624C22×C4C7×#4111yescharacteristic
625C22×C4C7×#4111yescharacteristic
626C22×C4C7×#4111yescharacteristic
627C22×C4C7×#4111yescharacteristic
628C22×C4C24×C711yescharacteristic
629Q16—28no—
630SD16—28no—
631SD16—28no—
632D8—28no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—22no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—41no—
644M16—41no—
645M16—41no—
646M16—41no—
647M16C2×C7×D414yes—
648M16C2×C7×D414yes—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C4⋊C4—22no—
662C4⋊C4—41no—
663C22⋊C4—22no—
664C22⋊C4—41no—
665C42—22no—
666C42—41no—
667C2×C7—21no—
668C2×C7—21no—
669C2×C7—21no—
670C2×C7—21no—
671C2×C7—21no—
672C2×C7—21no—
673C2×C7—21no—
674C2×C7—82no—
675C2×C7—82no—
676C2×C7C2×#39411yescharacteristic
677C23—22no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—81no—
684C23—82no—
685C23—82no—
686C23C7×#12111yescharacteristic
687C23C7×#12111yescharacteristic
688C23C7×#12311yescharacteristic
689C23C7×#12311yescharacteristic
690C23C7×#12411yescharacteristic
691C23C7×#12411yescharacteristic
692C23C2×C7×#4111yescharacteristic
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—82no—
733C2×C4C7×#12011yescharacteristic
734C2×C4C7×#12011yescharacteristic
735C2×C4C7×#12011yescharacteristic
736C2×C4C7×#12011yescharacteristic
737C2×C4C7×#12111yescharacteristic
738C2×C4C7×#12111yescharacteristic
739C2×C4C7×#12111yescharacteristic
740C2×C4C7×#12111yescharacteristic
741C2×C4C7×#12111yescharacteristic
742C2×C4C7×#12111yescharacteristic
743C2×C4C7×#12111yescharacteristic
744C2×C4C7×#12111yescharacteristic
745C2×C4C7×#12111yescharacteristic
746C2×C4C7×#12111yescharacteristic
747C2×C4C7×#12311yescharacteristic
748C2×C4C7×#12311yescharacteristic
749C2×C4C7×#12311yescharacteristic
750C2×C4C7×#12311yescharacteristic
751C2×C4C7×#12311yescharacteristic
752C2×C4C7×#12311yescharacteristic
753C2×C4C7×#12411yescharacteristic
754C2×C4C7×#12411yescharacteristic
755C2×C4C22×C7×D411yescharacteristic
756C2×C4C22×C7×D411yescharacteristic
757C2×C4C22×C7×D411yescharacteristic
758C2×C4C22×C7×D411yescharacteristic
759C2×C4C2×C7×#4111yescharacteristic
760C2×C4C2×C7×#4111yescharacteristic
761C8—24no—
762C8—24no—
763C8—42no—
764C8—42no—
765C7#2352511yescharacteristic, direct product factor, Sylow
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22C7×#39411yescharacteristic
782C22C7×#39411yescharacteristic
783C22C7×#39411yescharacteristic
784C22C7×#39411yescharacteristic
785C22C2×C7×#12111yescharacteristic
786C22C2×C7×#12311yescharacteristic
787C22C2×C7×#12411yescharacteristic
788C4—42no—
789C4—42no—
790C4—82no—
791C4C7×#39411yescharacteristic
792C4C7×#39411yescharacteristic
793C4C7×#39411yescharacteristic
794C4C7×#39411yescharacteristic
795C4C2×C7×#12011yescharacteristic
796C4C2×C7×#12111yescharacteristic
797C4C2×C7×#12111yescharacteristic
798C4C2×C7×#12311yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—82no—
808C2C2×C7×#39411yescharacteristic
subgroupG/H
centerC4×C7#394
commutator, Frattini, cosocleC22×C4C24×C7
socleC2×C7C2×#394
prime radicalC2×C7×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C7×#430C2semidirect
3. C2×C7×#421C2semidirect
4. C7×#2896C2semidirect
5. C2×C7×#413C2semidirect
6. C2×C7×#413C2semidirect
7. C7×#2049C2semidirect
8. C7×#2048C2semidirect
9. C2×C7×#344C2semidirect
27. C7×#430C22semidirect
32. C7×#419C22semidirect
33. C7×#418C22semidirect
41. C2×C7×#101C22semidirect
43. C2×C7×#100C22semidirect
44. C7×#344C22semidirect
45. #23525C7direct (N × H)
137. C2×#430C2×C7semidirect
138. C2×#421C2×C7semidirect
139. #2896C2×C7semidirect
140. C2×#413C2×C7semidirect
141. C2×#413C2×C7semidirect
142. #2049C2×C7semidirect
143. #2048C2×C7semidirect
144. C2×#344C2×C7semidirect
300. #430C22×C7semidirect
305. #419C22×C7semidirect
306. #418C22×C7semidirect
314. C2×#101C22×C7semidirect
316. C2×#100C22×C7semidirect
317. #344C22×C7semidirect
765. C7#23525direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#5752
C2×C7×#4302
C2×C7×#4212
C7×#28962
C2×C7×#4132
C7×#20492
C7×#20482
C2×C7×#3442
#235257